Final Exam ? Very good performance overall ? Essays were particularly good ? Mean - 88.5% ? Standard deviation - 5.7% 16.881 MIT Homework ?HW#8 – Mean = 96.1 – Standard Deviation = 7.4 ?HW#9 – Mean = 94.9 – Standard Deviation = 5.5 16.881 MIT The Remainder of the Course ? Primary mission -- Complete your term projects ? Secondary mission -- Cover topics of interest ? 70% of your grades are set (term project = 30%) ? Class sessions (half new topics / half consultation) – Tolerance Design / Projects – Mahalanobis Taguchi System / Projects – Conceptual Robust Design / Projects – Final Project Presentations 16.881 MIT Expectations on Final Project ? Should represent ~30 hours of effort ? Options – Full robust design effort – Planning phase only – Post mortem analysis of a previous effort – Study of an advanced topic in robust design – Other possibilities with permission 16.881 MIT Grading of the Final Project ? 75% Written report ? 25% Oral presentation ? Grading criteria include – Impact and significance of the results – Quality of the planning and analysis – Clarity of technical exposition 16.881 MIT Tolerance Design The Interface Between Design and Manufacture 16.881 MIT Outline ? History of tolerances ? Tolerancing standards ? Tolerance analysis ? Tolerance design ? Taguchi’s approach ?Case study 16.881 MIT History of Tolerances ? pre 1800 -- Craft production systems ? 1800 -- Invention of machine tools & the English System of manufacture ? 1850 -- Interchangeability of components & the American system of manufacture Jaikumar, Ramachandran. From Filing and Fitting to Flexible Manufacture, 1988. 16.881 MIT Craft Production ? Drawings communicated rough proportion and function ? Drawings carried no specifications or dimensions ? Production involved the master, the model, and calipers 16.881 MIT The English System ? Greater precision in machine tools ? General purpose machines – Maudslay invents the slide rest ? Accurate measuring instruments – Micrometers accurate to 0.001 inch ? Engineering drawings – Monge “La Geometrie Descriptive” – Orthographic views and dimensioning ? Parts made to fit to one another – Focus on perfection of fit 16.881 MIT The American System ? Interchangeability required for field service of weapons ? Focus on management of clearances ? Go-no go gauges employed to ensure fit ? Allowed parts to be made in large lots Go - no go gauges 16.881 MIT Tolerances on Drawings ? Binary acceptance criteria ? Multiple quality characteristics ? All criteria must be met (dominance) 16.881 12 MIT Basic Tolerancing Principles ref. ANSI Y14.5M ? Each dimension must have a tolerance ? Dimensions of size, form, and location must be complete ? No more dimensions than necessary shall be given ? Dimensions should not be subject to more than one interpretation ? Do not specify manufacturing method 16.881 MIT Tolerance Analysis Probabilistic Approaches ? Worst case stack up ? Root sum of squares ? Numerical integration ? Monte Carlo simulation 16.881 MIT Tolerance Analysis Problem 1.0”± 0.05” ? Extruded aluminum bar stock ? Cut two pieces ? Stacked end to end 1.0”± 0.1” ? What is the probability that the stack will fit in this bracket? MIT 16.881 2.2”± 0.1” Specifying Tolerances to Minimize Required Precision ? How should this part be dimensioned? ? How is optimal dimensioning determined by function? 16.881 MIT Tolerance Analysis Geometric / Kinematic Issues ? Will these parts mate? ? Solution approaches – Kinematic modeling – Assembly simulation 16.881 MIT Variation Systems Analysis You supply geometry You define distributions Software provides: Variance Defect rate Pareto diagram MIT Computer Aided Tolerancing ? Strengths – Requires few probabilistic assumptions – Can account for real assembly considerations ? Tooling ?Gravity – Integrated with many CAD environments ? Major Pitfalls – Compliance of parts – Source of input data 16.881 MIT Process Capability Indices p(q) UL? 2 L UL U q + 2 ? ? Process Capability Index C p ≡ ( UL ) /2 3σ UL+ μ ? ? Bias factor k ≡ 2 (UL) / 2? ? Performance Index C pk ≡ C p (1 ? k ) 16.881 20 MIT Tolerance Cost Models p(q) Cost Machining cost Scrap cost q L U UL+ 2 UL? 2 Tolerance 16.881 MIT Tolerance Cost Models Multiple Processes Cost Machining Grinding Lapping Tolerance 16.881 MIT Traditional Tolerance Design ? Select tolerances on components that optimize profitability – Tighter tolerances - higher costs of manufacture – Looser tolerances - higher scrap rates ? Approaches – Linear programming – Discrete optimization 16.881 MIT Taguchi Tolerance Design ? Use OAs in a noise experiment to determine the magnitude of tolerance factor effect – How many levels would you choose? ? Use the quality loss function as a basis for the trade off between higher manufacturing costs and lower customer satisfaction 16.881 MIT Tolerance Design Case Study Who would you involve in the tolerance design study? Singh, K., R. Newton, and C. Zaas, “Tolerance Design on a Moveable Window System of an Automobile 16.881 Door”, ASI 3rd International Symposium, 1997. MIT Customer Requirements ? Smooth and quiet operation under all weather conditions ? Consistent closing and opening speeds ? No wind noise or water leakage ? Long life and high reliability 16.881 MIT System P-Diagram 16.881 Noise Factors & Levels ? Why use three level noise factors? ? Why is there a difference in spread of the levels between a three level and two level factor? 16.881 MIT Noise Factor Effects on Average Glass Velocity ? What is the significance of the range? ? What is the significance of non-linearity? 16.881 MIT Noise Factor Effects on Stall Force ? How would you use this to make a Pareto diagram? 16.881 MIT Window System Case Study Conclusions ? Cross functional team included design, manufacture, reliability, and suppliers ? Motor power and regulator efficiency identified as major contributors to variation ? Computer simulation allowed redesign prior to prototyping ? Product development cycle time and cost reduced 16.881 MIT Next Steps ? Next off-campus session – SDM Conference room 16.881 MIT References ? Evans, D. H., 1974, “Statistical Tolerancing: The State of the Art, Part 2. Methods of Estimating Moments,” Journal of Quality Technology, vol. 7, no. 1, pp.1-12. ? Bjorke, O., 1978, Computer Aided Tolerancing, Tapir Publishers, Trondheim, Norway. ? Harry, Mikel J., and J. Ronald Lawson, 1992, Six Sigma Producibility Analysis and Process Characterization, Addison Wesley, Reading, MA. 16.881 MIT References, Cont. ? ASME, 1983, ANSI Y14.5M -- Dimensioning and Tolerancing, Americain Society of Mechanical Engineering, New York. ? Craig, M., 1988, “Variation by Design,” Mechanical Engineering, vol. 110, no. 11, pp. 52- 54. ? Greenwood, W. H. and K. W. Chase, 1987, “A New Tolerance Analysis Method for Designers and Manufacturers,” ASME Journal of Engineering for Industry, vol. 109, pp. 112-116. 16.881 MIT References, Cont. ? Jaikumar, Ramachandran, 1988, From Filing and Fitting to Flexible Manufacture, working paper 88-045. ? Keeler, Stephen P., Alan K. Jones, and Harold A. Scott, 1994, "Tolerancing Methods and Software: A Status Report," Document No. BCSTECH-94-030, Boeing Computer Services, Seattle, WA. ? Lee, W. J., and T. C. Woo, 1989, "Optimum Selection of Discrete Tolerances," ASME Journal of Mechanisms, Transmissions, and Automation in Design, vol. 111, pp. 243-251. 16.881 MIT References, Cont. ? Ostwald, P. F., and J. Huang, 1977, "A Method for Optimal Tolerance Selection," ASME Journal of Engineering for Industry, vol. 99, pp. 558-565. ? Whitney, D. E., O.L.Gilbert,andM., Jastrzebski, 1994, “Representation of Geometric Variations Using Matrix Transforms for Statistical Tolerance Analysis in Assemblies,” Research in Engineering Design, vol. 6, pp. 191-210. 16.881 MIT